### Some articles on *hereditarily finite, finite, hereditarily*:

**Hereditarily Finite**Set

... In mathematics and set theory,

**hereditarily finite**sets are defined recursively as

**finite**sets consisting of 0 or more

**hereditarily finite**sets ...

**Hereditarily Finite**Set - Formal Definition

... A recursive definition of a

**hereditarily finite**set goes as follows Base case The empty set is a

**hereditarily finite**set ... Recursion rule If a1...ak are

**hereditarily finite**, then so is {a1...ak} ... The set of all

**hereditarily finite**sets is denoted Vω ...

Hereditary Property - In Set Theory

... A couple of notions are defined analogously A

... A couple of notions are defined analogously A

**hereditarily finite**set is defined as a**finite**set consisting of zero or more**hereditarily finite**sets ... Equivalently, a set is**hereditarily finite**if and only if its transitive closure is**finite**... A**hereditarily**countable set is a countable set of**hereditarily**countable sets ...### Famous quotes containing the word finite:

“All *finite* things reveal infinitude:”

—Theodore Roethke (1908–1963)

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